Confronting Seiberg's duality with r duality in N=1 supersymmetric QCD

Systematizing our results on r duality obtained previously we focus on comparing r duality with the generalized Seiberg duality in the r vacua of N=2 and N=1 super-Yang-Mills theories with the U(N) gauge group and N _f matter flavors (N _f>N). The number of condensed (s)quarks r is assumed to be in the interval 23N _f<r≤N. To pass to N=1 we introduce an N=2-breaking deformation, a mass term μ for the adjoint matter, eventually decoupling the adjoint matter in the limit of large μ. If one starts from a large value of the parameter ξ∼μm, where the original theory is at weak coupling, and let ξ decrease, one hits a crossover transition from weak to strong coupling (here m is a typical value of the quark masses). Below this transition the original theory is described in terms of a weakly coupled infrared-free r dual theory with the U(N _f-r) gauge group and N _f light quarklike dyon flavors. Dyon condensation leads to confinement of monopoles, defying a naive expectation of quark confinement. The quarks and gauge bosons of the original theory are in an "instead-of- confinement" phase. The r and Seiberg dualities are demonstrated to coincide in the r=N vacua. In the 23N _f<r<N vacua two dualities do not match. In this window Seiberg's dual is at strong coupling while our r-dual model is at weak coupling. Thus, we can speak of triality. Seiberg's dual solution at weak coupling reappears again at r<N _f-N<13N _f.